Correlations For Effective Thermal Conductivity Research Articles

Comprehensive effective thermal conductivity correlation and fast model for the melting of a phase change material inside a horizontal shell-and-tube unit

The effective thermal conductivity is a robust alternative to include the effect of natural convection during the melting of a phase-change material, while solving only the energy equation. With this approach, significant time savings may be obtained, maintaining satisfactory accuracy. However, it remains unclear how well the existing equations predict the enhanced conductivity for horizontal shell-and-tube heat exchangers, particularly in terms of accurately estimating the liquid fraction. In this paper, a simplified model for the melting of a phase-change material is developed based on the pure conduction formulation while considering natural convection. The model was solved using the finite volume method and implemented in Python. A previously validated computational fluid dynamics (CFD) model was used to calculate the enhanced conductivity, which was then applied to the simplified model. The simplified model was found to be 3500 times faster than the CFD model, with a maximum deviation of only 8.2%. Subsequently, existing correlations to predict the effective thermal conductivity were assessed. The results for the liquid fraction predictions indicated maximum deviations ranging from 33.6% to 144.8%, for predictors developed under melting conditions, and from 35.6% to 231.1%, for equations developed without considering phase-change. Further, new correlations, spanning all melting regimes, were proposed, revealing maximum deviations of 17.73% and 10.24% for the different scenarios evaluated. Therefore, the new correlations demonstrated to be the preferred choice to obtain more accurate models for the melting of phase-change materials inside horizontal shell-and-tube units.

Improved effective thermal conductivity of sand bed in thermal energy storage systems

Thermal energy storage (TES) is becoming increasingly important in the modern energy landscape. As the global energy demand continues to rise and the integration of renewable energy becomes crucial, there is a growing need for sustainable and affordable ways to store energy. TES materials, such as sand, molten salts and heat transfer fluids, are a significant contributing factor to the cost-effective characteristics of TES systems. In recent advancements, sand has been viewed as a high-potential TES material for TES applications, attributed to its thermal resistance, widespread availability, safety, and affordability. However, the low thermal conductivity of sand remains a challenge for some TES applications. This study evaluates different correlations for effective thermal conductivity in a sand-based experimental study where the best correlation was adapted for a numerical simulation of the sand bed. The study further explores the use of discarded metallic chips to enhance the thermal conductivity of the sand. Our experiments assessed two integration techniques using three distinct metallic materials. It was found that the maximum heat rate could be achieved with 20 % (volumetric basis) of aluminium chips mixed in sand (1.7 times that of pure sand).

Significance of Inclined MHD on Hybrid Nanoliquid Flow in an Annulus Using Modified Buongiorno Model in the Presence of Two Different Heat Sources: Response Surface Methodology

In this modern fluid field technology, hybrid nanoliquid are of great interest to researchers because of their thermal properties which provide superior heat transfer improvements compared to nanoliquid. Thus, in this study, the heat and mass transport characteristics in a horizontal annular duct filled with the water-based Cu–Al2O3 hybrid nanoliquid is analyzed using the modified Buongiorno model (two-phase model). The two different heat sources namely, temperature-related heat source (THS) and exponential space-related heat source (ESHS) are analyzed in thermal analysis. An inclined magnetism and viscous dissipation aspects are also taken into account. The correlation for effective thermal conductivity and viscosity are modeled by utilizing the experimental work of Corcione. The coupled nonlinear equations were solved numerically using the finite difference method. Further, the heat transport rate is optimized using the response surface methodology (RSM). The significance of effective parameters on the flow structure, thermal pattern, concentration field, heat and mass transport rate are visualized through two-dimensional (2D) and three-dimensional (3D) surface plots. It is noticed that the chaotic motion of nanoparticles advances the thickness of the thermal and solutal boundaries. The velocity field has an inverse association with the applied magnetic field and its angle of inclination. The consequence of the Reynolds number is favorable for the velocity and temperature fields. The heat transport is more dominated by the Reynolds number compared to the chaotic motion of nanoparticles and thermophoretic aspect. Furthermore, the sensitivity of the Nusselt number to the Reynolds number, chaotic motion of nanoparticles and thermophoretic aspect are always negative.

An effective thermal conductivity correlation for three high-temperature chloride salts melting in a spherical thermal storage capsule

ABSTRACT Chloride salts are viable phase change materials (PCMs) for packed-bed thermal energy storage for third-generation concentrating solar power (CSP) systems. In the study, a two-dimensional, axisymmetric and transient model is developed to simulate the constrained melting process of three chloride salts (NaCl-CaCl2, LiCl and MgCl2) in a spherical capsule while considering the natural convection of the salt. The simulation results lead to the proposal of an effective thermal conductivity correlation for the liquid part of these three PCMs’ melting process in a sphere, represented as λ eff/λ l = 0.38Ra 0.26(δ/R i)0.25. Additionally, a simplified conduction-controlled numerical model has been developed for predicting the melting process of chloride salts in a spherical capsule with improved accuracy and efficiency. The proposed correlation improves the conduction-controlled model’s accuracy in predicting the melting process compared to other correlations previously reported in literature. The proposed correlation comprehensively reflects the conduction and natural convection of the chloride salts during the constrained melting process in a sphere.

Experimental investigation on the effective thermal conductivities of different hydrate-bearing sediments

The natural gas hydrate has been regarded as an important future green energy. Significant progress on the hydrate exploitation has been made, but some challenges are still remaining. In order to enhance the hydrate exploitation efficiency, a significant understanding of the effective thermal conductivity (ETC) of the hydrate-bearing sediment has become essential, since it directly controls the heat and mass transfer behaviors, and thereby determines the stability of hydrate reservoir and production rate. In this study, the effective thermal conductivities of various hydrate-bearing sediments were in-situ measured and studied. The impacts of temperature, particle size and type of sediment were investigated. The effective thermal conductivities of the quartz sand sediments before and after hydrate formation were in-situ measured. The results show the weak negative correlation of effective thermal conductivity of the quartz sand sediment on the temperature before and after the hydrate formation. The effective thermal conductivity of the hydrate-bearing sediment decreases with the increase of particle size of the sediment. The dominant effect of the type of porous medium on the characteristics of the effective thermal conductivity of hydrate-bearing sediment was highlighted. The results indicate that both the effective thermal conductivities of hydrate-bearing quartz sand sediment and hydrate-bearing silicon carbide sediment are weakly negatively correlated with temperature, but the effective thermal conductivity of hydrate-bearing clay sediment is weakly positively dependent on the temperature. In addition, the values of the effective thermal conductivities of various hydrate-bearing sediments are in the order of hydrate-bearing silicon carbide sediment > hydrate-bearing quartz sand sediment > hydrate-bearing clay sediment. These findings could suggest that the intrinsic thermal conductivity of porous medium could control the characteristics of effective thermal conductivity of hydrate-bearing sediment.

Generalized correlation for effective thermal conductivity of high porosity architectured materials and metal foams

This paper presents a numerical study on the effective thermal conductivity (keff) of architectured materials typically realized through additive manufacturing. Four different unit cell topologies- Cube, Octet, Face-diagonal Cube, and Tetrakaidecahedron, were simulated for a range of porosity values, and both solid- and fluid-phase thermal conductivities. Numerically predicted keff values were validated against the in-house experiments carried out on single-cell thick 5 × 5 unit cell arrangement samples. These simulations led to a correlation for keff as a function of lattice porosity and thermal conductivities of solid- and fluid-phase materials. For the solid-to-fluid thermal conductivity ratio (ks/kf) greater than 300, the keff showed dependence on only the solid thermal conductivity for any given porosity and unit cell topology. The proposed correlation for the keff of architectured materials is applicable to all the four unit cell topologies with porosities > 0.8, and ks/kf ranging from 102 to 104. For these parameters, the correlation can also predict the keff of high-porosity metal foams obtained via foaming process with an accuracy of ±10%.

New Equivalent Thermal Conductivity Model for Size-Dependent Convection-Driven Melting of Spherically Encapsulated Phase Change Material.

Spherically encapsulated phase change materials (PCMs) are extensively incorporated into matrix material to form composite latent heat storage system for the purposes of saving energy, reducing PCM cost and decreasing space occupation. Although the melting of PCM sphere has been studied comprehensively by experimental and numerical methods, it is still challenging to quantitatively depict the contribution of complex natural convection (NC) to the melting process in a practically simple and acceptable way. To tackle this, a new effective thermal conductivity model is proposed in this work by focusing on the total melting time (TMT) of PCM, instead of tracking the complex evolution of solid–liquid interface. Firstly, the experiment and finite element simulation of the constrained and unconstrained meltings of paraffin sphere are conducted to provide a deep understanding of the NC-driven melting mechanism and exhibit the difference of melting process. Then the dependence of NC on the particle size and heating temperature is numerically investigated for the unconstrained melting which is closer to the real-life physics than the constrained melting. Subsequently, the contribution of NC to the TMT is approximately represented by a simple effective thermal conductivity correlation, through which the melting process of PCM is simplified to involve heat conduction only. The effectiveness of the equivalent thermal conductivity model is demonstrated by rigorous numerical analysis involving NC-driven melting. By addressing the TMT, the present correlation thoroughly avoids tracking the complex evolution of melting front and would bring great convenience to engineering applications.

ANFIS modelling of effective thermal conductivity of ethylene glycol and water nanofluids for low temperature heat transfer application

Nanofluids have been proven to be promising coolants for heat transfer application due to their superior thermal properties. In the present work, experimental studies were carried out to investigate the thermal conductivity of ethylene glycol (EG) and water mixture (35:65 v/v in ratio) based CuO, Al2O3 and TiO2 nanofluids. The study has considered nanofluid containing nanoparticles in the concentration range of 0.2 to 2 wt%. The effect of nanoparticle concentration on thermal conductivity was investigated in terms of effective thermal conductivity (ratio of thermal conductivity of nanofluid to that of base fluid) at low temperatures (5 to 25 °C). Results indicated significant improvement in thermal conductivity at lower temperature of nanofluids. Enhancement of 6.34%, 4.87% and 3.59% in thermal conductivity was obtained for 2 wt% of concentration at 5 °C for CuO, Al2O3 and TiO2 nanoparticles respectively compared to EG:Water. Correlations for effective thermal conductivity were developed by regression considering two input (temperature, concentration) and three input (temperature, concentration and nanoparticles thermal conductivity) parameters using experimental results. An intelligent model, adaptive neuro-fuzzy inference system (ANFIS) approach was used to model the effective thermal conductivity of nanofluids. ANFIS model performed better than the correlations developed.

Significance of nonlinear Boussinesq approximation and non-uniform heat source/sink on nanoliquid flow with convective heat condition: sensitivity analysis

The quadratic convective flow of nanoliquid over an elongating plate subjected to non-uniform heat source/sink, partial slip, and Newton boundary conditions is studied by using the modified Buongiorno model. The correlation for effective thermal conductivity and viscosity of nanoliquid are taken from the experimental work of Corcione. The dimensionless velocity, temperature, rate of heat transport, and mass transport distributions are simulated by solving the nonlinear boundary value problem using the finite difference method. The additional novelty of the present study is an application of response surface methodology to scrutinize the interactive impact of key parameters on the rate of heat transfer. Further, the influence of key parameters is deliberated on various flow fields using the surface and streamline plots. The higher velocities are noticed for the case of nonlinear Boussinesq approximation as compared with the usual Boussinesq approximation. The temperature enhances with a non-uniform heat source/sink aspect. The sensitivity of the heat transfer to the nanoparticle volume fraction remains positive.

Two‐phase study of nanofluids mixed convection and entropy generation in an I‐shaped porous cavity with triangular hot block and different aspect ratios

The nanofluids mixed convection in a porous I‐shaped cavity using Buongiorno's method of nanofluids simulation is reported in this paper. The nanofluids have been assumed as a mixture of water and TiO2 nanoparticles up to 4% of volume concentration. Having accurate prediction of thermal properties of nanofluids is crucial for a numerical solution. Thus, a new predictive correlation for effective thermal conductivity is developed using the multivariable regression method with a high accuracy compared to the experimental data. Six different problems, including two different porous media and three different aspect ratios of the cavity, are solved implementing the finite volume method. As the first time, an internal triangular hot block in a cavity has been studied. The results showed that the entropy generation reduces with any increase in the aspect ratio of the cavity and the nanoparticle volume concentration. Any increase in the nanoparticle volume concentration also leads to enhance the average Nusselt number, in all considered aspect ratios.

A New Thermal Conductivity Model and Two-Phase Mixed Convection of CuO-Water Nanofluids in a Novel I-Shaped Porous Cavity Heated by Oriented Triangular Hot Block.

This paper investigates the cooling performance of nanofluid (NF) mixed convection in a porous I-shaped electronic chip with an internal triangular hot block using Buongiorno’s two-phase model. This type of cavity and hot block geometry has not been studied formerly. The NF was assumed to be a mixture of water and CuO nanoparticles (NP) up to 4% of volume concentration. As most published mathematical models for the thermal conductivity of NF give inaccurate predictions, a new predictive correlation for effective thermal conductivity was also developed with a high accuracy compared to the experimental data. The results showed that any increase in the NP volume concentration enhances the average Nusselt number () and the normalized entropy generation, and reduces the thermal performance of the cavity in all orientations of the hot block. The maximum enhancement in cooling performance was 17.75% and occurred in the right-oriented hot block in the sand-based porous cavity. Furthermore, adding the NP to the base fluid leads to a more capable cooling system and enhances the irreversibility of the process.

Validation of a melting fraction-based effective thermal conductivity correlation for prediction of melting phase change inside a sphere

It is complicated and costly to directly simulate the natural convection influenced melting processes involving multiple PCM units in packed bed phase change system. An effective method to simulate such melting process is using an equivalent conduction model, in which the effective thermal conductivity (ETC) of PCM considering the natural convection effects is an important thermal parameter needing to be determined. In this paper, the ETC of PCM is investigated and determined by comparing numerical results based on models considering natural convection and pure conduction, respectively. Parameters of interest include melting fraction (α), Rayleigh number (Ra, 1.5 × 104 ≤ Ra ≤ 6.3 × 107), Prandtl number (Pr, 17 ≤ Pr ≤ 550) and Stefan number (Ste, 0.011 ≤ Ste ≤ 0.276.). Results show that the ETC of PCM has a strong relation to α and Ra, while it has little relation to Pr and Ste. Hence, an ETC correlation is developed as a function of Ra and α. Validation and application of the ETC correlation are further carried out, and it is found that the melting fraction predicted based on the present ETC correlation can better reflect the effect of liquid zone geometry on the melting heat transfer with natural convection than that predicted based on the previously reported correlations using a liquid gap parameter.

Development of correlations for effective thermal conductivity of a tetrakaidecahedra structure in presence of combined conduction and radiation heat transfer

The variations in the total effective thermal conductivity (keff,t) of a tetrakaidecahedra unit cell structure as functions of porosity (ϕ), thermal conductivity of the solid phase (ks) and the average temperature of the medium (Tavg), in the presence of combined conduction and radiation heat transfer, are presented in this article. For this purpose, the governing energy conservation equation is numerically solved using the blocked-off region approach based on the finite volume method. In addition, the variations in the radiative properties of the structure as functions of surface reflectivity (ρs), pore density (PPC) and ϕ are investigated, for which, a pure radiation heat transfer based numerical model is developed and used. From the detailed numerical simulations, three different correlations for keff,t are proposed. Correlation 1 is developed by fitting the raw simulated data, although its form does not respect some of the limiting conditions. Particularly for ks<5W/mK and in the absence of thermal radiation, it under-predicts the effective thermal conductivity due to pure heat conduction (keff,PC). Correlation 2, on the other hand, satisfies all possible limiting conditions, although it requires one additional simulation or correlation for keff,PC. Finally, correlation 3 is obtained by superposing the effective thermal conductivities due to pure radiation (keff,R) and keff,PC, while introducing an adjustable coefficient in order to account for the coupling between them. From the investigation on radiative properties, it is observed that the extinction coefficient increases with the decrease in ϕ and with the increase in PPC as well as ρs and hence keff,t as well as keff,R is expected to decrease for these conditions.

A novel effective thermal conductivity correlation of the PCM melting in spherical PCM encapsulation for the packed bed TES system

Packed bed thermal energy storage (TES) system with phase change material (PCM) encapsulation is one of the potential TES technologies for the solar thermal application. In present study, the constrained melting process of PCM in spherical encapsulation is simulated by a validated natural convection included model. This model is then used to simulate the melting processes of NaNO3 with different conditions. Meanwhile, the same melting processes are also calculated by the conduction controlled model with available effective thermal conductivity correlations reported in the literature. It is found that the changes of liquid fraction obtained from the natural convection included model and the conduction controlled model with the reported thermal conductivity correlations show obvious difference. Then, based on the simulating results of the cases using the natural convection included model, a new correlation for the effective thermal conductivity is proposed by linear regression. It shows that the conduction controlled model with the proposed effective thermal conductivity correlation gives better results on the change of liquid fraction than that with correlations reported in the literature. Therefore, the proposed correlation can be used to calculate the melting process of PCM in a capsule by the conduction controlled model, which is in urgent need for modeling of packed bed latent TES systems.

Thermal conductivity correlations of open-cell foams: Extension of Hashin–Shtrikman model and introduction of effective solid phase tortuosity

Open-cell foams have emerged as promising materials for use in heat sink and heat exchanger applications. The thermal behavior of open-cell foams depends on their microscopic structure. The effective thermal conductivity of open-cell porous foams can be measured using experimental techniques, predicted from the 3-D direct numerical simulations on reconstructed foam structures obtained from micro-computed tomography images or derived from idealized structure thermal analysis. Based on the tetrakaidecahedron unit cell and different strut morphologies, three dependent and interdependent empirical correlations for effective thermal conductivity were derived. They encompass all morphological parameters and ratios of constituent phases of foams of different materials.In this process, the Hashin–Shtrikman (HS) bounds model was first extended and applied to the resistor model. A correlation term, Ω was introduced to take into account the thermal conductivities of constituent phases and the morphological parameters of the foam structure. Secondly, a more complex effective model that is a combination of series and parallel models was derived by introducing effective solid phase tortuosity. Lastly, a simple model (KT-model) was derived that can be used to predict either effective thermal conductivity or intrinsic solid phase conductivity depending upon which one of these quantities is known. The present study clearly demonstrates that the proposed empirical correlations yield extremely accurate estimates of the effective thermal conductivity for all the experimental and numerical data of different foam materials reported in the literature.

Thermal conductivity measurement of thermochemical storage materials

Thermal properties related to heat and mass transfer are crucial when designing thermochemical heat storage systems. Therefore, enhancing this phenomenon lies in the thermal conductivity of the used material. The effective thermal conductivity of salt hydrates and host matrices is measured using two different methods by differential scanning calorimeter from 100 to 200 °C and radial flow apparatus called guarded hot cartridge from 20 to 70 °C, where the method effect is less than 12%. On this latter, the results as function of temperature was modelled and theoretical correlation of effective thermal conductivity of the material bed presented. Four inorganic salts often used in thermochemical energy storage (CaCl2, MgCl2, SrBr2 and MgSO4) and host matrices (activated carbon, expanded natural graphite and silica gel) were used as samples and the results on both systems for only salts give a thermal conductivity in the range of 0.3–1.3 W m−1 K−1 with measurement uncertainty less than 14%. These obtained data are satisfactory with literature values. Regarding the results, the need of composite design is mandatory to achieve great thermal performances in thermal storage systems, especially in closed systems. The presented results can be used for the evaluation and the improvement of heat and mass transfer in thermochemical and sorption heat storage systems.

A critical review on heat transfer in trickle bed reactors

AbstractA critical review of the available information about heat transfer between a packed bed with cocurrent downflow of gas and liquid and an external medium was undertaken. Several aspects such as experimental set-ups and methods employed to study heat transfer in trickle bed reactors, models used to interpret experimental data, and literature correlations of heat transfer parameters are addressed. From the analysis of the available experimental information, a refined database has been built, which allows comparing the performance of the existing correlations for the parameters of the extensively employed two-dimensional pseudohomogeneous plug flow model (i.e., effective radial thermal conductivity and wall heat transfer coefficient). In addition, new correlations for effective thermal conductivity have been developed. Identification of gaps in the current knowledge and recommendations for future works are summarized.

Estimating Correlation of Effective Thermal Conductivity on the Spherical Packed Bed Porous Media

The correlation of an effective thermal conductivity (keff) on spherical packed bed porous media with stagnant fluid was proposed. Alumina-Cordierite ceramic ball (Al-Co) having average diameter (d) of 2.1 cm and porosity (Φ) of 0.468 was examined. The experimental procedure was operated based on ASTM E1225. The tested porous sample was sandwiched by references materials (Solid Brass, 70%Cu, 30%Zn). A higher temperature (TH) on the top of test set was obtained from wire heater with a constant electrical power of 350 W. The water cooling set was installed at the bottom of to generate a lower temperature (TL). Four previous models established from geometrical structure were compared to validate the present correlation. From experiment, it was found that keff decreased with increasing TH. Thus, the relation between keff and TH was appropriately proposed by a correlating linear-equation (keff/kf = 329.2(1-0.1028(TH/100)). Agreement between the present correlation and literature models was satisfied particular.

Experimental Investigation of Convective Heat Transfer in Circulating Water System

The laminar convective heat transfer behavior of CuO nanoparticle dispersions in water with three different particle sizes (23 nm, 51 nm, and 76 nm) is investigated experimentally in a flow loop with constant heat flux. The main purpose of this study is to evaluate the effect of particle size on convective heat transfer in laminar region. The experimental results show that the suspended nanoparticles remarkably increase the convective heat transfer coefficient of the base fluid, and the nanofluid with 23nm particles shows higher heat transfer coefficient than nanofluids containing the other two particle sizes about 10% under the same Re. Based on the effective medium approximation and the fractal theory, the effective thermal conductivity of suspension is obtained. It is shown that if the new effective thermal conductivity correlation of the nanofluids is used in calculating the Prandtl and Nusselt numbers, the new correlation accurately reproduces the convective heat transfer behavior in tubes.

A critical synthesis of thermophysical characteristics of nanofluids

A critical synthesis of the variants within the thermophysical properties of nanofluids is presented in this work. The experimental results for the effective thermal conductivity and viscosity reported by several authors are in disagreement. Theoretical and experimental studies are essential to clarify the discrepancies in the results and in proper understanding of heat transfer enhancement characteristics of nanofluids. At room temperature, it is illustrated that the results of the effective thermal conductivity and viscosity of nanofluids can be estimated using the classical equations at low volume fractions. However, the classical models fail to estimate the effective thermal conductivity and viscosity of nanofluids at various temperatures. This study shows that it is not clear which analytical model should be used to describe the thermal conductivity of nanofluids. Additional theoretical and experimental research studies are required to clarify the mechanisms responsible for heat transfer enhancement in nanofluids. Correlations for effective thermal conductivity and viscosity are synthesized and developed in this study in terms of pertinent physical parameters based on the reported experimental data.